Abstract :
The looseness image of a triangulation G on a closed surface image is defined as the minimum number k such that for any surjection image, there exists a face image of G which gets three distinct colors image, image and image. We define image and image as the minimum and the maximum of image taken over all triangulations image on image isomorphic to G as graphs. We shall show that image, where image stands for the Euler characteristic image, and in particular that two triangulations on the projective plane have the same looseness if they are isomorphic as graphs.
